After introducing the main ideas and reviewing some of the literature on the subject, we consider a discrete non-local variational model for clustering in the context of soft-classification semi-supervised learning. The functional is inspired by a similar model studied by Alberti and Bellettini (see ) in the context of phase transition for ferromagnetic materials. A parameter ϵncontrols both the non-local term, as well as the size of the phase transition layer. We identify the G-limit of the variational functional as ϵn→ 0. In the machine learning community, this is known as the study of the consistency of the model. The limiting functional is given by a fidelity term plus weighted anisotropic perimeter.
|Number of pages||25|
|Journal||Rendiconti del Seminario Matematico|
|Publication status||Published - 2019|
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